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Math Help - What does notation max{ a : b } means?

  1. #1
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    What does notation max{ a : b } means?

    I dont know where to post this question. In information theory Capacity C = max{I(Xk;Yk) : E[Xk^2]=P} where maximization is wrt probability fx prob. density fn of Xk. What does this value C equals? Can anyone explain that notation. -Devanand T
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    Re: What does notation max{ a : b } means?

    The curly braces seem to be the set-builder notation,
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    Re: What does notation max{ a : b } means?

    max{ a : b } means it return you a max value in a , b

    max (10,9) = 10

    max(2,9) = 9
    Last edited by skeeter; July 26th 2012 at 07:22 AM.
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    Re: What does notation max{ a : b } means?

    Quote Originally Posted by Neeraj View Post
    max{ a : b } means it return you a max value in a , b

    max (10,9) = 10

    max(2,9) = 9
    Can you explain why you think that this interpretation is more likely than the one in post #2?
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    Re: What does notation max{ a : b } means?

    Quote Originally Posted by dexterdev View Post
    I dont know where to post this question. In information theory Capacity C = max{I(Xk;Yk) : E[Xk^2]=P} where maximization is wrt probability fx prob. density fn of Xk. What does this value C equals? Can anyone explain that notation. -Devanand T
    My best guess is this: maximize the mutual information between Xk and Yk, subject to the constraint that the expected value of Xk^2 is P.

    As far as I know (I don't know much about channel capacity), the part about the expected value of Xk^2 is not part of the standard definition of channel capacity. See, for example, Channel capacity - Wikipedia, the free encyclopedia
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